If A is an n × n matrix, then the permanent of A, denoted by per A, is defined as \(\displaystyle \mbox{per } A = \sum _{\sigma \in S_n} \prod _{i=1}^n a_{i\sigma (i)}, \) where S n is the set of permutations of 1, 2, …, n. Thus the definition of the permanent is similar to that of the determinant except that all the terms in the expansion have a positive sign.